General exact solvability conditions for the initial value problems for linear fractional functional differential equations

Natalia Dilna

Archivum Mathematicum (2023)

  • Issue: 1, page 11-19
  • ISSN: 0044-8753

Abstract

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Conditions on the unique solvability of linear fractional functional differential equations are established. A pantograph-type model from electrodynamics is studied.

How to cite

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Dilna, Natalia. "General exact solvability conditions for the initial value problems for linear fractional functional differential equations." Archivum Mathematicum (2023): 11-19. <http://eudml.org/doc/298969>.

@article{Dilna2023,
abstract = {Conditions on the unique solvability of linear fractional functional differential equations are established. A pantograph-type model from electrodynamics is studied.},
author = {Dilna, Natalia},
journal = {Archivum Mathematicum},
keywords = {fractional order functional differential equations; Caputo derivative; normal and reproducing cone; unique solvability},
language = {eng},
number = {1},
pages = {11-19},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {General exact solvability conditions for the initial value problems for linear fractional functional differential equations},
url = {http://eudml.org/doc/298969},
year = {2023},
}

TY - JOUR
AU - Dilna, Natalia
TI - General exact solvability conditions for the initial value problems for linear fractional functional differential equations
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 1
SP - 11
EP - 19
AB - Conditions on the unique solvability of linear fractional functional differential equations are established. A pantograph-type model from electrodynamics is studied.
LA - eng
KW - fractional order functional differential equations; Caputo derivative; normal and reproducing cone; unique solvability
UR - http://eudml.org/doc/298969
ER -

References

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  1. Aphithana, A., Ntouyas, S.K., Tariboon, J., 10.1186/s13661-015-0329-1, Bound. Value Probl. 2015 (68) (2015), 14 pp., https://doi.org/10.1186/s13661-015-0329-1. (2015) MR3338722DOI10.1186/s13661-015-0329-1
  2. Diethelm, K., The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo Type, Springer, 2010. (2010) Zbl1215.34001MR2680847
  3. Dilna, N., Exact solvability conditions for the model with a discrete memory effect, International Conference on Mathematical Analysis and Applications in Science and Engineering, Book of Extended Abstracts, 2022, 405–407 pp. (2022) 
  4. Dilna, N., Fečkan, M., 10.3390/math10101759, Mathematics 10 (10) (2022), 1759, https://doi.org/10.3390/math10101759. (2022) MR4563012DOI10.3390/math10101759
  5. Dilna, N., Gromyak, M., Leshchuk, S., 10.1007/s10958-022-06072-8, J. Math. Sci. 265 (2022), 577–588, https://doi.org/10.1007/s10958-022-06072-8. (2022) MR4518887DOI10.1007/s10958-022-06072-8
  6. Fečkan, M., Marynets, K., 10.1140/epjst/e2018-00017-9, The European Physical Journal Special Topics 226 (2017), 3681–3692, https://doi.org/10.1140/epjst/e2018-00017-9. (2017) DOI10.1140/epjst/e2018-00017-9
  7. Fečkan, M., Wang, J.R., Pospíšil, M., Fractional-Order Equations and Inclusions, 1st. ed., Walter de Gruyter GmbH, Berlin, Boston, 2017. (2017) 
  8. Gautam, G.R., Dabas, J., 10.1007/s13348-016-0189-8, Collect. Math 69 (2018), 25–37. (2018) MR3742978DOI10.1007/s13348-016-0189-8
  9. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Elsevier B.P., 2006. (2006) Zbl1092.45003MR2218073
  10. Opluštil, Z., 10.1007/s11072-009-0038-8, Nonlinear Oscil. 11 (3) (2008), 365–386. (2008) MR2512754DOI10.1007/s11072-009-0038-8
  11. Patade, J., Bhalekar, S., 10.1515/psr-2016-5103, Phys. Sci. Rev. Inform. 9 (2017), 20165103 https://doi.org/10.1515/psr-2016-5103. (2017) DOI10.1515/psr-2016-5103
  12. Reed, M., Simon, B., Methods of modern mathematical physics, Acad. Press, New York-London, 1972. (1972) 
  13. Rontó, A., Rontó, M., Successive Approximation Techniques in Non-Linear Boundary Value Problems, Handbook of Differential Equations: Ordinary Differential Equations, Elsevier, New York, 2009, pp. 441–592. (2009) MR2440165
  14. Šremr, J., 10.21136/MB.2007.134126, Math. Bohem. 132 (2007), 263–295. (2007) MR2355659DOI10.21136/MB.2007.134126

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